Shahadah: One of the five pillars of Islam

Q: The good word is one of the five pillars of Islam.
Did the Messenger (peace be upon him) teach us that the good word is La ilaha illa Allah Muhammad rasul Allah (there is no god but Allah. Muhammad is the Messenger of Allah), or just La ilaha illa Allah (there is no god but Allah)? What do the Glorious Qur'an and books of Sahih (authentic) Hadiths tell us in this regard? If the Qur'an mentions the first formula, which Surah is it in? What is the number of the Ayah (Qur'anic verse)? Likewise, if the reliable books of Hadith confirm it, where can it be found? Please, mention the book, the page, and the categorical degree of relevant Hadith? Finally, do Muslims have the right to add any word (Part No. 1; Page No. 96) or sentence to any Ayah or Sahih Hadith specially if the addition is good and acceptable? What is the Shari`ah (Islamic law) ruling on this?

The answer is as follows:
A:
The good word is La ilaha illa Allah as you have mentioned in the question. It is one of the foundations upon which Islam is built. Furthermore, it is the first of its pillars. The Prophet (peace be upon him) taught us this word and the other five pillars as well. He (Peace be upon him) says:
Islam is based on five pillars: Testimony that La ilaha illa Allah Muhammad rasul Allah (there is no god but Allah. Muhammad is the Messenger of Allah); performing Salah (Prayer), giving Zakah (obligatory charity), performing Hajj (Pilgrimage), and observing Sawm (Fast) in Ramadan.
(Related by
Ahmad,
Al-Bukhari ,
Muslim ,
Al-Nasa'y , and
Al-Tirmidhy
on the authority of
Ibn `Umar 'may Allah be pleased with them both'). The Prophet (peace be upon him) also says:
I have been commanded to fight people until they testify that there is no god but Allah and I am the Messenger of Allah. If they say so, their lives and property become inviolable unless justified by law and then their reckoning will be by Allah.
(Related by the six Compilers of Hadiths 'Imams Al-Bukhari, Muslim, Abu Dawud, Al-Tirmidhy, Al-Nasa'y, and Ibn Majah')
Ibn `Abbas (may Allah be pleased with them both) related that when Allah's Messenger (Peace be upon him) sent
Mu`adh to
Yemen, he said to him:
You will go to the people of the Book. First of all, invite them to testify that `there is no deity but Allah'.
In another narration:
call them to believe in Tawhid (Oneness of Allah). If they accept this, then tell them that Allah has enjoined five Salahs (Prayers) in every day and night upon them. If they accept this, tell them that Allah has obliged them to pay Zakah (obligatory charity) taken from the rich and distributed among the poor. If they obey this, then avoid taking the best of their possessions. Beware of injustice, for there is no barrier between an oppressed person's Du`a' (supplication) and Allah i.e. It is definitely answered.
(Part No. 1; Page No. 97)
(Related by
Al-Bukhari and
Muslim).
Allah (Exalted be He) commands us to obey Him and act upon the Shari`ah conveyed by His Messenger Muhammad (Peace be upon him) whether it is from the Qur'an or the Sunnah (whatever is reported from the Prophet). Allah (the Exalted) says:
Say (O Muhammad صلى الله عليه وسلم): "Obey Allâh and the Messenger (Muhammad صلى الله عليه وسلم)." But if they turn away, then Allâh does not like the disbelievers.
Allah also says:
He who obeys the Messenger (Muhammad صلى الله عليه وسلم), has indeed obeyed Allâh
and also says:
And whatsoever the Messenger (Muhammad صلى الله عليه وسلم) gives you, take it; and whatsoever he forbids you, abstain (from it).
Muslims have no right to add a ruling, a word, a sentence, or anything to the Qur'an or the Sunnah of the Prophet (Peace be upon him). This would be an act of Bid`ah (a rejected innovation in religion). It is authentically reported that the Prophet (Peace be upon him) said:
Whoever brings about extraneous things to our religion, his act is rejected.
In another narration:
Whoever does an act for which there is no sanction from our behalf, it is to be rejected.
.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.